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Prime Poisson suspensions

Published online by Cambridge University Press:  04 August 2014

FRANÇOIS PARREAU  and
EMMANUEL ROY
FRANÇOIS PARREAU
Affiliation:
Laboratoire Analyse Géométrie et Applications, UMR 7539, Université Paris 13, 99 avenue J.B. Clément, F-93430 Villetaneuse, France email parreau@math.univ-paris13.fr, roy@math.univ-paris13.fr
EMMANUEL ROY
Affiliation:
Laboratoire Analyse Géométrie et Applications, UMR 7539, Université Paris 13, 99 avenue J.B. Clément, F-93430 Villetaneuse, France email parreau@math.univ-paris13.fr, roy@math.univ-paris13.fr
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Abstract

We establish a necessary and sufficient condition for a Poisson suspension to be prime. The proof is based on the Fock space structure of the $L^{2}$-space of the Poisson suspension. We give examples of explicit infinite measure-preserving systems, in particular of non-singular compact group rotations that give rise to prime Poisson suspensions. We also compare some properties of so far known prime transformations with those of our examples, showing that these examples are new.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 7 , October 2015 , pp. 2216 - 2230
Copyright
© Cambridge University Press, 2014 

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